Vincent de Leijster

96 Chapter 5 We followed the same approach to test whether ecosystem services also followed a saturating response trajectory, by testing with the Michaelis-Menten model or with linear, generalized linear or sigmoid models if better fitting. We used Akaike Information Criterion (AIC) to interpret best model fit. For the variable farmer-reported coffee yield, we first used a Cook’s distance test to identify outliers, as this variable was not measured but obtained through the survey. In case outliers were detected, we transformed the data and generalized its distribution. In case the transformed variable distribution was not yet following a normal distribution, we excluded outliers identified by Cook’s distance (coffee yield >700 kg/ha, n=2). Then we tested the fit using GLM with a Gamma distribution, as the data was still right-skewed. We analyzed the data in R version 3.6.1 (R Core Team, 2019) using packages ‘tidyverse’ and ‘nlstools’ and ‘lme4’. 5.2.5.2 Ecosystem service bundle development and trade-offs We tested the development of the relations between pairs of ecosystem services using pair-wise correlations for two time periods, between 0-10 y and between 11-20 y after implementation of agroforestry. Since we had information on multiple indicators per ecosystem service and several of them were naturally correlated, we selected between highly correlated indicators for the same ecosystem service. This is to prevent accounting twice for the same effect, for example, for coffee provisioning we had two related quantitative variables (plot-level productivity and farm-level yield) and therefore used coffee yields, and for carbon we used above-ground and below-ground but not total carbon. Moreover, we did not include butterfly indicators and leaf cutter ant damage, due to smaller sample sizes than the rest of the data. For the latter, we used information of all farms, including the monoculture plantations. We used Pearson correlation tests using the R-package ‘psych’. 5.2.5.3 Factors explaining ecosystem service supply We examined confounding factors that influenced ecosystem service supply after transition to agroforestry. To do this, we excluded the monoculture coffee farms (Table 5-1). We avoided doubling effects and mismatches in sample sizes by selecting ecosystem services as explained in section 5.2.5.2, and we standardized the indicators for ecosystem services using the ecosystem service index approach presented in Kearney et al. (2017). In these standardization calculations potential soil loss and coffee berry borer incidence were inversed to obtain a more-is-better scale. We used a principal component analysis to define the ecosystem service bundles and reduce the dimensionality of the ecosystem